The Proof that the Standard Transformations of E and B are not the Lorentz Transformations. Application to Motional EMF

摘要

In this paper it is proved by using the Clifford algebra formalism that thestandard transformations (ST) of the three-dimensional (3D) vectors of theelectric and magnetic fields E and B are not the Lorentz transformations (LT)of well-defined quantities from the 4D spacetime. This difference between theST and the LT is obtained regardless of the used algebraic objects (1-vectorsor bivectors) for the representation of the electric and magnetic fields in theusual observer dependent decompositions of F. The LT correctly transform thewhole 4D quantity, e.g., E_{f}=F\cdot \gamma_{0}, whereas the ST are the resultof the application of the LT only to the part of E_{f}, i.e., to F, but leavinggamma_{0} unchanged. The new decompositions of F in terms of 4D quantities thatare defined without reference frames, i.e., the absolute quantities, areintroduced and discussed. It is shown that the LT of the 4D quantitiesrepresenting electric and magnetic fields correctly describe the motionalelectromotive force (emf) for all relatively moving inertial observers, whereasit is not the case with the ST of the 3D E and B.